We develop a heterogeneous-agent New Keynesian model featuring a frictional labor market with on-the-job search to quantitatively study the role of worker flows in inflation dynamics and monetary policy. Motivated by our empirical finding that the historical negative correlation between the unemployment rate and the employer-to-employer (EE) transition rate up to the Great Recession disappeared during the recovery, we use the model to quantify the effect of EE transitions on inflation in this period. We find that the four-quarter inflation rate would have been 0.6 percentage points higher between 2016 and 2019 if the EE rate increased commensurately with the decline in unemployment. We then decompose the channels through which a change in EE transitions affects inflation. We show that an increase in the EE rate leads to an increase in the real marginal cost, but the direct effect is partially mitigated by the equilibrium decline in market tightness through aggregate demand that exerts downward pressure on the marginal cost. Finally, we study the normative implications of job mobility for monetary policy responding to inflation and labor market variables according to a Taylor rule, and find that the welfare cost of ignoring the EE rate in setting the nominal interest rate is 0.2 percent in additional lifetime consumption.